Question: Given $ m \angle RPS = 3x + 110$, and $ m \angle QPR = 8x - 73$, find $m\angle QPR$. $P$ $Q$ $S$ $R$
From the diagram, we see that together ${\angle QPR}$ and ${\angle RPS}$ form ${\angle QPS}$ , so $ {m\angle QPR} + {m\angle RPS} = {m\angle QPS}$ Since $\angle QPS$ is a straight angle, we know ${m\angle QPS = 180}$ Substitute in the expressions that were given for each measure: $ {8x - 73} + {3x + 110} = {180}$ Combine like terms: $ 11x + 37 = 180$ Subtract $37$ from both sides: $ 11x = 143$ Divide both sides by $11$ to find $x$ $ x = 13$ Substitute $13$ for $x$ in the expression that was given for $m\angle QPR$ $ m\angle QPR = 8({13}) - 73$ Simplify: $ {m\angle QPR = 104 - 73}$ So ${m\angle QPR = 31}$.